Open-source mathematical tool detects gerrymandering

Gerrymandering is the practice of establishing a political advantage by manipulating the boundaries of electoral districts. This involves diluting the opposing party’s voters by spreading them among many districts and concentrating them into a small number of districts to reduce their influence in other districts. Gerrymandering can result in the formation of electoral districts with absurd shapes difficult to justify.

An article in Harvard Data Science Review describes improvements to the mathematical methodology behind a tool called GerryChain, which is intended to detect gerrymandering.

The tool detects likely cases of gerrymandering by creating a “pool” of alternate electoral district maps which also meet legal voting criteria, such as having a similar number of voters in each district. This pool of districts can be used to demonostrate when proposed districts are extremely different to the plans generated automatically and therefore are likely to have been drawn with political goals in mind.

GerryChain was initially created by Washington State University mathematician Professor Daryl DeFord in 2018 for the Voting Rights Data Institute. In an earlier iteration, it was used to analyse district maps proposed for elections to the Virginia House of Delegates, which a federal court had ruled as having been subjected to unconstitutional racial gerrymanders.

“We wanted to build an open-source software tool and make that available to people interested in reform, especially in states where there are skewed baselines,” said DeFord, who is co-lead author of the study. “It can be an impactful way for people to get involved in this process, particularly going into this year’s redistricting cycle where there are going to be a lot of opportunities for pointing out less than optimal behaviour.”

The new paper focuses on how the mathematical and computational models implemented in GerryChain can be used to put proposed districts into context by creating samples of alternative valid plans to compare them with. These plans can be used when a voting plan is challenged in court as gerrymandered. The proposed Virginia House of Delegates districts plan had 12 voting districts with a Black voting age population at or above 55 per cent; comparing this against a pool of alternative legal plans showed the proposal was an extreme outlier of what was possible and therefore extremely likely to have been drawn with the intenion of reducing the influence of Black voters.

One of the biggest challenges to creating voting maps are the sheer number of possibilities, DeFord said: “There are more feasible plans in a lot of states than there are molecules in the universe. That's why you want this kind of mathematical tool.”

The GerryChain tool uses a method called a spanning tree recombination: to create an alternative voting map, the method involves taking two districts, merging them together, before splitting them apart again in a different way. This creates a greater change, with multiple voting blocks changing at a time. It can create many alternative plans within a matter of hours or days and is open for anyone to use.

However, the authors say that computers shouldn’t be relied on to create final voting plans; rather that this method provides a tool for analysing baselines and evaluating potential alternatives.

“This is not some sort of magic black box where you push the button and you get a collection of perfect plans,” said DeFord. “It really requires serious engagement with social scientists and legal scholars. Because the rules are written and implemented by people, this is a fundamentally human process.”